Sinkhorn divergence (REF ) has several important properties. First, it
satisfies all axioms for a metric with the exception of identity of
indiscernibles (or the coincidence axiom), that is, it satisfies
non-negativity, symmetry, and triangle inequality axioms
[1]}.
Second, it is convex and smooth with respect to the input probability
vectors and can be differentiated using automatic differentiation [2]}.
Third, as discussed below, it can be computed by a simple alternating
minimization algorithm, known as Sinkhorn's algorithm, where each
iteration involves two matrix-vector products.
Consequently, Sinkhorn divergence may serve as a feasible alternative
to classical Waaserstein distance, particularly when probability
measures are supported on multi-dimensional metric spaces.
